Rav Bodner of the Laws of Brochos makes a distinction between cultivated and wildly grown. According to him, hearts of palm that come from Brazil are wildly grown and would receive a Shehakol, while hearts of palm from Ecuador are cultivated and would receive a Ha’adoma.

While it is true that the Shulchan Aruch cited by Alex says to make a shehakol, the reasoning given in the mishna berurah is using outdated metzius, since hearts of palm is an industry where trees are specifically planted to harvest the fibers. Although I have no source, I would venture to say it is haetz since that is the only produce that the farmers intend on harvesting from the tree and thereby becomes its main fruit, despite the fact that the tree may have the potential to grow other fruits.

Yahu, I can't find your answer. Are you asking a lashon kasha? Peri just means that it is edible as a food. It need not be a separate product given off by the tree to be called peri. A raya to this is the Rosh's psak that smelling cinnamon (which is bark) gets a "reiach tov lepeiros". The mashmaos of the reasoning for our psak (to make atzei besamim) is that cinnamon is not a besem leachila (its an enhancer).
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YDKJun 22 '10 at 5:24

Shulchan Aruch (Orach Chaim 204:1) says Shehakol. Mishnah Berurah (ibid. :9) explains that even though it grows from the ground (and thus by rights ought to be Ha'adamah), it is downgraded because "people don't plant a tree with the intention of eating this part when it's soft, since that prevents the branches from growing."